{"paper":{"title":"From Approximate Factorization to Root Isolation with Application to Cylindrical Algebraic Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Kurt Mehlhorn, Michael Sagraloff, Pengming Wang","submitted_at":"2013-01-21T14:14:07Z","abstract_excerpt":"We present an algorithm for isolating the roots of an arbitrary complex polynomial $p$ that also works for polynomials with multiple roots provided that the number $k$ of distinct roots is given as part of the input. It outputs $k$ pairwise disjoint disks each containing one of the distinct roots of $p$, and its multiplicity. The algorithm uses approximate factorization as a subroutine.\n  In addition, we apply the new root isolation algorithm to a recent algorithm for computing the topology of a real planar algebraic curve specified as the zero set of a bivariate integer polynomial and for iso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4870","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}